sin² (x/2) = 1 - cos x
                     2

cos 2(x/2) = cos² (x/2) - sin² (x/2)

cos x = 1 - sin² (x/2) - sin² (x/2)

cos x = 1 - 2sin² (x/2)

2sin² (x/2) = 1 - cos x

sin² (x/2) = 1 - cos x
                     2